Dynamically driven correlations in elastic net models reveal sequence of events and causality in proteins

Abstract

An explicit analytic solution is given for the Langevin equation applied to the Gauss-ian Network Model of a protein subjected to both a random and a deterministic peri-odic force. Synchronous and asynchronous components of time correlation functionsare derived and an expression for phase differences in the time correlations of resi-due pairs is obtained. The synchronous component enables the determination ofdynamic communities within the protein structure. The asynchronous componentreveals causality, where the time correlation function between residues i and j differsdepending on whether i is observed before j or vice versa, resulting in directionalinformation flow. Driver and driven residues in the allosteric process of cyclophilin Aand human NAD-dependent isocitrate dehydrogenase are determined by a perturba-tion-scanning technique. Factors affecting phase differences between fluctuations ofresidues, such as network topology, connectivity, and residue centrality, are identi-fied. Within the constraints of the isotropic Gaussian Network Model, our resultsshow that asynchronicity increases with viscosity and distance between residues,decreases with increasing connectivity, and decreases with increasing levels of eigen-vector centrality.